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When calculating VIX, how to deal with the problem of asymmetry of put and call data?

This is perhaps a bit of a stretch but how about inferring the value of the puts by using the put-call parity principle?
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Delta hedging when volatility is stochastic

How to Delta Hedge and the PnL is indeed affect if real volatility is not constant (either deterministic ou stochastic). The exactly difference will depends on the model choose. I don't recall this ...
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3 votes

Reduced volatility in local stochastic volatility model

why do you reduce or flatten the volatility surface in order to calibrate the stochastic volatility ? This is a crude way of creating a partial volsurface, which is lower than the actual market vol ...
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